SOLUTION: Describe two laws of exponents and provide an example illustrating each law.

Question 126172: Describe two laws of exponents and provide an example illustrating each law.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Exponent Law # 1:

Let's say you have the expression . Now, if you want to square this entire expression, you would simply say

To go even further, you can use an exponent law that states:
In other words, when you have 2 exponents (ie one exponent is raised to another exponent), you simply multiply the two exponents and that product will become the new exponent.

Start with the given expression

Use the previous identity to rewrite the expression. So we're simply going to multiply the exponents 3 and 2

Multiply

Now raise 2 to the 6th power to get 64

So what we've shown is that

Notice how . So

So this example illustrates and supports the identity

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Exponent Law # 2:

Now let's say you have the expression

and you want to multiply that by

One way you could do it is simply note that and

When you multiply and , you get

OR

You can use the identity

This identity basically says that if you multiply two expressions that have the same base, you can simply add the two exponents

So in our case

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